A Volterra kernel approach to non-linear functional connectivity
The availability of multi-electrode arrays makes it possible to record (or infer with EEG/MEG) evoked activity simultaneously at multiple, possibly interconnected brain sites. We are developing a method of assessing linear and non-linear functional connectivity between sites that combines graphical models and a Volterra kernel analysis of responses driven by external stimuli and endogenous signals of local origin. In this approach, the output of a node in the graph is a function of its inputs from one or more external stimuli or from other nodes in the graph. In addition, each node can have its own endogenous activity (local noise) that can contribute to the measured nodal output. The goal of the method is, for a given graph, to identify each node?s functional operator in terms of a multi-input Volterra series representation. Externally evoked activity alone is sometimes all that is necessary to completely characterize a graph and its nodal operators. However, in other cases, externally evoked activity may not be able to fully tease apart (even theoretically) the internal functional operators. Here, local noise, which differs between nodes and acts as a ?stimulus? to downstream activity, can further (and sometimes completely) pin down the operators.
To the extent that external inputs force the system into a particular operational configuration, the computed operators reflect that configuration. The effective system results from non-linear interaction between external inputs and endogenous signals that are generated locally at each node. The method fully models both evoked as well as endogenous activity, yielding a more accurate estimation of the nodal operators.
In the context of functional connectivity, this non-linear method subsumes causality measures that are based on linear regression. It improves on the more general all-but-one (conditional) Granger optimization procedure (multivariate autoregression or other measures), giving a better result without having to do separate calculations that remove nodal connections one at a time. Finally, the method characterizes connectivity in terms of operator descriptions as well as probability measures.
We have also used a bivariate version of the method to detect non-linear functional connectivity between pairs of EEG electrodes. Importantly, the method cleanly isolates true neural interactions from volume conduction effects. Volume conduction appears at zero latency in the first-order kernel.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). A Volterra kernel approach to non-linear functional connectivity.
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.085
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Received:
02 Feb 2009;
Published Online:
02 Feb 2009.